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Book/Report | FZJ-2017-04740 |
1971
Kernforschungsanlage Jülich, Verlag
Jülich
Please use a persistent id in citations: http://hdl.handle.net/2128/15071
Report No.: Juel-0781-PP
Abstract: A numerical solution of the non-linear Vlasov equation in one dimension is carried out by the Fourier-Fourier transformation method for the case of an inhomogeneous plasma. The initial electron distribution function consists of a background Maxwellian plasma plus two Maxwellian bumps at $\pm$ $v_{b}$ which appear only in the central region of the plasma. The magnitude of the bumps are linear functions of x within this central region, having a maximum strength D at the center. The ions are assumed immobile and are chosen so that at t = 0, the plasma is neutral. Perfectly reflecting walls are used as boundary conditions at x = 0 and L. The linear equation is also solved numerically and compared with the linear solution obtained by the method of Landau poles. The macroscopic variables of density N (x, t), average velocity $\overline{V}$ (x, t) and pressure P (x, t) are recovered at specified time intervals. The microscopic movement of particles is also followed and plotted as the difference between the initial and t = $t_{o}$ distribution functions.
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